1270 - Smeech

Time Limit : 1 Second

Memory Limit : 128 MB

Submission: 134

Solved: 26

Description
Professor Octastichs has invented a new programming language, Smeech. An expression in Smeech may be a positive or negative integer, or may be of the form (p e1 e2) where p is a real number between 0 and 1 (inclusive) and e1 and e2 are Smeech expressions. The value represented by a Smeech expression is as follows: An integer represents itself With probability p, (p e1 e2) represents x + y where x is the value of e1 and y is the value of e2; otherwise it represents x - y. Given a Smeech expression, what is its expected value?
Input
Input consists of several Smeech expressions, one per line, followed by a line containing ().
Output
For each expression, output its expected value to two decimal places.
sample input
7
(.5 3 9)
()
sample output
7.00
3.00
hint
source
waterloo 29 September, 2007
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